TRACT 37.

OF GUNNERY.

247

the squares of the same, which is one power less; and theresistances being also, in this case, as the squares of the ve-locities, we must therefore increase the squares of the ve-locity in the ratio of the diameters of the balls; that is, as2 id:: 252 1 : 3l752d = v 1 , and hence v = 178 Vd, is ageneral value of the greatest velocity for any ball whosediameter is d inches.

69. If we take here the 3lb ball, belonging to the secondtable of resistances, nearty, the diameter d being = 2-773 ;then v'2‘773 = 1-666, and 178 X P666 = 297, is the great-est or uniform velocity, with which the 3lb ball will descend.And if we take the 6lb ball, whose diameter is 3-494 inches,as in the third table of resistances nearly: then sj 3-494 =1‘870, and 178 y. 1-870 = 333, being the greatest velocitythat can be acquired by the 6lb ball, and with which it willafterwards uniformly descend. For a 9lb ball, whose dia-meter is 4-00, the velocity will be 178 x 2 = 356. And soon for any other size of iron ball, as in the following table.

Wt.

lbs.

Diarn.

inches

Termin.Velocityv, feet

Heightdue to v,feet

Times offreelyfalling

i

1-923

247

948

7-72

2

2-423

277

1193

8-66

3

2-773

297

1371

9-28

4

3-053

311

1503

9-72

6

3-494

333

1724

10-41

9

4-000

356

1970

11-12

12

4-403

374

2174

11-69

18

5-040

400

2488

12-50

24

5-546

419

2729

13-09

32

6-106

440

3010

13-75

36

6-350

449

3134

14-03

42

6-684

461

3304

14*50

Where the first column contains the weight of the balls mlbs; the 2d their diameters in inches; the 3d their ve oci lesto which they nearly approach, as a limit, and therefore calledtheir terminal or last velocities, with which they afterwarddescend uniformly; and the 4th column the heights due to